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In the upright posture, venous outﬂow is considerably less pulsatile
(57%) and occurs predominantly through the vertebral plexus, while in
the supine posture venous outﬂow occurs predominantly through the
internal jugular veins. A slightly lower tCBF (12%), a considerably
smaller CSF volume oscillating between the cranium and the spinal
canal (48%), and a much larger ICC (2.8-fold) with a corresponding
decrease in the MRI-derived ICP values were measured in the sitting
position. [1]

I don't quite get the answer though. I know that the cerebral blood flow distribution is more complex than we think, but does the overall blood flow increase or decrease with an upright posture?

The characteristic features are that after standing up for 60 s, the pressure (both systolic and diastolic values) drops signiﬁcantly from a mean pressure of approximately 95 mmHg to a mean pressure of approximately 58 mmHg. At the same time, the blood ﬂow velocity also decreases followed by an increase. However, it should be noted that while the mean velocity decreases, the decrease is not as big, because of a large widening of the pulse-amplitude (systolic value minus diastolic value).

Although our studies have not revealed a quantitative relationship between alterations in the arterial pressure and cerebral blood flow in the same
person, there was a definite fall in cerebral blood
flow with the fall in effective cerebral arterial
pressure on standing.

There was no statistically significant change in CPP, CBF, cerebral metabolic rate of oxygen, arteriovenous difference of lactate, or cerebrovascular resistance associated with the change in head position. The data indicate that head elevation to 30° significantly reduced ICP in the majority of the 22 patients without reducing CPP or CBF.

This means that Inter-Cranial Pressure (ICP) was significantly reduced in most patients without reducing Cerebral Blood Flow (CBF). This means changes in pressure do not always equate to changes in blood flow of the same relative magnitude.

Reading more into those articles will give you more insight into the complexities of how the flow changes in posture, but unless you have a more specific question I believe that covers what you asked.